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The dog is a wolf-like canid.[7][8][9] The genetic divergence between the dog's ancestor and modern wolves occurred between 40,000 and 30,000 years ago, just before or during the Last Glacial Maximum[2][1] (20,000–27,000 years ago). This timespan represents the upper time-limit for the commencement of domestication because it is the time of divergence but not the time of domestication, which occurred later.

https://en.wikipedia.org/wiki/Domestication_of_the_dog

We domesticated them roughly twice as far back as we domesticated cats (12,000y). Cats became domesticated alongside the use of agriculture. Cats started spending time around humans because agriculture brought prey for them (rodents, etc) to places where humans resided.